What is magnetic flux?

In order to give an accurate quantitative formulation of Faraday's law of electromagnetic induction, it is necessary to introduce a new value - the flux of the magnetic induction vector.

The magnetic induction vector characterizes the magnetic field at each point in space. You can introduce another value that depends on the values ​​of the vector not at one point, but at all points of the surface bounded by a flat closed contour.

To do this, consider a flat closed conductor (circuit), limiting the surface area S and placed in a uniform magnetic field (Fig. 2.4). The normal (vector whose modulus is equal to one) to the plane of the conductor makes an angle with the direction of the magnetic induction vector. The magnetic flux Ф (flux of the magnetic induction vector) through a surface with an area S is a value equal to the product of the modulus of the magnetic induction vector by the area S and the cosine of the angle between the vectors and:

The product is a projection of the magnetic induction vector onto the normal to the contour plane. That's why

The magnetic flux is greater, the greater B n and S. The value of Ф is called "magnetic flux" by analogy with the flow of water, which is the greater, the more more speed water flow and pipe cross-sectional area.

The magnetic flux can be graphically interpreted as a quantity proportional to the number of lines of magnetic induction penetrating a surface of area S.

The unit of magnetic flux is weber. in 1 weber (1 Wb) is created by a uniform magnetic field with an induction of 1 T through a surface of 1 m 2 located perpendicular to the magnetic induction vector.

The magnetic flux depends on the orientation of the surface that the magnetic field penetrates.

Generalized information about magnetic flux

Today's lesson in physics with us is devoted to the topic of magnetic flux. In order to give an accurate quantitative formulation of Faraday's law of electromagnetic induction, we will need to introduce a new quantity, which is actually called the magnetic flux or flux of the magnetic induction vector.

From the previous classes, you already know that the magnetic field is described by the magnetic induction vector B. Based on the concept of the induction vector B, we can find the magnetic flux. To do this, we will consider a closed conductor or circuit with an area S. Suppose a uniform magnetic field with induction B passes through it. Then the magnetic flux F the magnetic induction vector through a surface with an area S is the value of the product of the modulus of the magnetic induction vector B and the area of ​​the circuit S and by cos the angle between the vector B and the normal cos alpha:

In general, we have come to the conclusion that if we place a circuit with a current in a magnetic field, then all the lines of induction of this magnetic field will pass through the circuit. That is, we can safely say that the line of magnetic induction is this very magnetic induction, which is located at every point of this line. Or we can say that the lines of magnetic induction are the flux of the induction vector along the space limited and described by these lines, i.e. magnetic flux.

And now let's remember what the unit of magnetic flux equals:

Direction and amount of magnetic flux

But it is also necessary to know that each magnetic flux has its own direction and quantitative value. In this case, we can say that the circuit penetrates a certain magnetic flux. And also, it should be noted that the magnitude of the magnetic flux also depends on the size of the circuit, that is, the larger the size of the circuit, the greater the magnetic flux will pass through it.

Here we can summarize and say that the magnetic flux depends on the area of ​​space through which it passes. If, for example, we take a fixed frame of a certain size, which is penetrated by a constant magnetic field, then in this case the magnetic flux that passes through this frame will be constant.

With an increase in the strength of the magnetic field, the magnetic induction will naturally increase. In addition, the magnitude of the magnetic flux will also increase proportionally, depending on the increased magnitude of the induction.

Practical task

1. Look carefully at this figure and give an answer to the question: How can the magnetic flux change if the circuit rotates around the OO" axis?

2. How do you think, how can the magnetic flux change if we take a closed circuit, which is located at a certain angle to the lines of magnetic induction, and its area is halved, and the vector module is quadrupled?
3. Look at the answer options and tell me how to orient the frame in a uniform magnetic field so that the flux through this frame is zero? Which of the answers will be correct?

4. Look carefully at the drawing of the depicted circuits I and II and give an answer, how can the magnetic flux change during their rotation?

5. What do you think determines the direction of the induction current?
6. What is the difference between magnetic induction and magnetic flux? Name these differences.
7. What is the formula for the magnetic flux and the quantities that are included in this formula.
8. What methods of magnetic flux measurement do you know?

It's interesting to know

Did you know that increased solar activity affects the Earth's magnetic field and approximately every eleven and a half years it increases in such a way that it can disrupt radio communications, cause compass failure and adversely affect human well-being. Such processes are called magnetic storms.

Myakishev G. Ya., Physics. Grade 11: textbook. for general education institutions: basic and profile. levels / G. Ya. Myakishev, B. V. Bukhovtsev, V. M. Charugin; ed. V. I. Nikolaev, N. A. Parfenteva. - 17th ed., revised. and additional - M.: Education, 2008. - 399 p.: ill.

Among the many definitions and concepts associated with a magnetic field, one should highlight the magnetic flux, which has a certain direction. This property is widely used in electronics and electrical engineering, in the design of instruments and devices, as well as in the calculation of various circuits.

The concept of magnetic flux

First of all, it is necessary to establish exactly what is called magnetic flux. This value should be considered in combination with a uniform magnetic field. It is homogeneous at every point of the designated space. A certain surface, which has some fixed area, denoted by the symbol S, falls under the action of a magnetic field. The field lines act on this surface and cross it.

Thus, the magnetic flux Ф, crossing the surface with area S, consists of a certain number of lines coinciding with the vector B and passing through this surface.

This parameter can be found and displayed as the formula Ф = BS cos α, in which α is the angle between the normal direction to the surface S and the magnetic induction vector B. Based on this formula, one can determine the magnetic flux with maximum value at which cos α \u003d 1, and the position of the vector B will become parallel to the normal perpendicular to the surface S. And, conversely, the magnetic flux will be minimal if the vector B is located perpendicular to the normal.

In this version, the vector lines simply slide along the plane and do not cross it. That is, the flux is taken into account only along the lines of the magnetic induction vector crossing a specific surface.

To find this value, weber or volt-seconds are used (1 Wb \u003d 1 V x 1 s). This parameter can be measured in other units. The smaller value is the maxwell, which is 1 Wb = 10 8 µs or 1 µs = 10 -8 Wb.

Magnetic field energy and magnetic induction flux

If an electric current is passed through a conductor, then a magnetic field is formed around it, which has energy. Its origin is associated with the electric power of the current source, which is partially consumed to overcome the EMF of self-induction that occurs in the circuit. This is the so-called self-energy of the current, due to which it is formed. That is, the energies of the field and current will be equal to each other.

The value of the self-energy of the current is expressed by the formula W \u003d (L x I 2) / 2. This definition is considered equal to the work that is done by a current source that overcomes the inductance, that is, the self-induction EMF and creates a current in the electrical circuit. When the current stops acting, the energy of the magnetic field does not disappear without a trace, but is released, for example, in the form of an arc or spark.

The magnetic flux that occurs in the field is also known as the flux of magnetic induction with a positive or negative value, the direction of which is conventionally indicated by a vector. As a rule, this flow passes through a circuit through which an electric current flows. With a positive direction of the normal relative to the contour, the direction of current movement is a value determined in accordance with . In this case, the magnetic flux generated by the circuit with electric shock, and passing through this contour, will always have a value greater than zero. Practical measurements also point to this.

The magnetic flux is usually measured in units established by the international SI system. This is the already known Weber, which is the magnitude of the flow passing through a plane with an area of ​​1 m2. This surface is placed perpendicular to the magnetic field lines with a uniform structure.

This concept is well described by the Gauss theorem. It reflects the absence of magnetic charges, so the induction lines are always represented as closed or going to infinity without beginning or end. That is, the magnetic flux passing through any kind of closed surfaces is always zero.

1. The principle of active radar.
2. Pulse radar. Principle of operation.
3. Basic timing of the operation of a pulsed radar.
4. Types of radar orientation.
5. Formation of a sweep on the PPI radar.
6. The principle of operation of the induction log.
7. Types of absolute lags. Hydroacoustic Doppler log.
8. Flight data recorder. Description of work.
9. Purpose and principle of AIS operation.
10.Transmitted and received AIS information.
11. Organization of radio communication in AIS.
12. The composition of the AIS ship equipment.
13. Structural diagram of the ship's AIS.
14. The principle of operation of the GPS SNS.
15. Essence of GPS differential mode.
16.Sources of errors in GNSS.
17. Structural diagram of the GPS receiver.
18. The concept of ECDIS.
19. ENC classification.
20. Appointment and properties of the gyroscope.
21. The principle of operation of the gyrocompass.
22. The principle of operation of a magnetic compass.

Electronic thermometers are widely used as temperature meters. You can get acquainted with contact and non-contact digital thermometers on the website http://mera-tek.ru/termometry/termometry-elektronnye. These devices mainly provide temperature measurement at technological installations due to the high measurement accuracy and high recording speed.

In electronic potentiometers, both indicating and recording, automatic current stabilization in the potentiometer circuit and continuous thermocouple compensation are used.

Conductor connection- part of the technological process of connecting the cable. Stranded conductors with a cross-sectional area from 0.35 to 1.5 mm 2 are connected by soldering after twisting the individual wires (Fig. 1). If they are restored with insulating tubes 3, then before twisting the wires, they must be put on the core and moved to the cut of the sheath 4.

Rice. 1. Connection of cores by twisting: 1 - conductive core; 2 - core insulation; 3 - insulating tube; 4 - cable sheath; 5 - tinned wires; 6 - soldered surface

Solid conductors they are overlapped, fastened before soldering with two bandages of two or three turns of tinned copper wire with a diameter of 0.3 mm (Fig. 2). You can also use special terminals wago 222 415, which today have become very popular due to ease of use and reliability of operation.

When installing electrical actuators, their housing must be grounded with a wire with a cross section of at least 4 mm 2 through the grounding screw. The connection point of the grounding conductor is thoroughly cleaned, and after connection, a layer of CIATIM-201 grease is applied to it to protect it from corrosion. At the end of the installation, with the help of check the value, which should be at least 20 MΩ, and the grounding device, which should not exceed 10 Ω.

Rice. 1. Diagram of electrical connections of the sensor block of a single-turn electric mechanism. A - amplifier unit BU-2, B - magnetic sensor unit, C - electric actuator

21.03.2019

Types of gas analyzers

Using gas in furnaces, various devices and installations, it is necessary to control the process of its combustion in order to ensure safe operation and efficient operation of the equipment. At the same time, the qualitative and quantitative composition gas environment determined using devices called

The picture shows a uniform magnetic field. Homogeneous means the same at all points in a given volume. A surface with area S is placed in the field. Field lines intersect the surface.

Determination of magnetic flux:

The magnetic flux Ф through the surface S is the number of lines of the magnetic induction vector B passing through the surface S.

Magnetic flux formula:

here α is the angle between the direction of the magnetic induction vector B and the normal to the surface S.

It can be seen from the magnetic flux formula that the maximum magnetic flux will be at cos α = 1, and this will happen when the vector B is parallel to the normal to the surface S. The minimum magnetic flux will be at cos α = 0, this will be when the vector B is perpendicular to the normal to the surface S, because in this case the lines of the vector B will slide over the surface S without crossing it.

And according to the definition of magnetic flux, only those lines of the magnetic induction vector that intersect a given surface are taken into account.

The magnetic flux is measured in webers (volt-seconds): 1 wb \u003d 1 v * s. In addition, Maxwell is used to measure the magnetic flux: 1 wb \u003d 10 8 μs. Accordingly, 1 μs = 10 -8 wb.

Magnetic flux is a scalar quantity.

ENERGY OF THE MAGNETIC FIELD OF THE CURRENT

Around a conductor with current there is a magnetic field that has energy. Where does it come from? The current source included in the electric circuit has an energy reserve. At the moment of closing the electric circuit, the current source expends part of its energy to overcome the action of the emerging EMF of self-induction. This part of the energy, called own energy current, and goes to the formation of a magnetic field. The energy of the magnetic field is equal to the self-energy of the current. The self-energy of the current is numerically equal to the work that the current source must do to overcome the self-induction EMF in order to create a current in the circuit.

The energy of the magnetic field created by the current is directly proportional to the square of the current strength. Where does the energy of the magnetic field disappear after the current stops? - stands out (when a circuit with a sufficiently large current is opened, a spark or arc may occur)

4.1. The law of electromagnetic induction. Self-induction. Inductance

Basic Formulas

The law of electromagnetic induction (Faraday's law):

, (39)

where is the induction emf; is the total magnetic flux (flux linkage).

The magnetic flux created by the current in the circuit,

where is the inductance of the circuit; is the current strength.

Faraday's law as applied to self-induction

The emf of induction that occurs when the frame rotates with current in a magnetic field,

where is the magnetic field induction; is the frame area; is the angular velocity of rotation.

solenoid inductance

, (43)

where is the magnetic constant; is the magnetic permeability of the substance; is the number of turns of the solenoid; is the sectional area of ​​the turn; is the length of the solenoid.

Open circuit current

where is the current strength established in the circuit; is the inductance of the circuit; is the resistance of the circuit; is the opening time.

The current strength when the circuit is closed

. (45)

Relaxation time

Examples of problem solving

Example 1

The magnetic field changes according to the law , where = 15 mT,. A circular conducting coil with a radius = 20 cm is placed in a magnetic field at an angle to the direction of the field (at the initial moment of time). Find the emf of induction that occurs in the coil at time = 5 s.

Solution

According to the law of electromagnetic induction, the emf of induction arising in the coil, where is the magnetic flux coupled in the coil.

where is the area of ​​the coil,; is the angle between the direction of the magnetic induction vector and the normal to the contour:.

Let's substitute the numerical values: = 15 mT,, = 20 cm = = 0.2 m,.

Calculations give .

According to Faraday's law, where, then, but, therefore.

The “–” sign indicates that the induction emf and the induction current are directed counterclockwise.

SELF-INDUCTION

Each conductor through which electric current flows is in its own magnetic field.

When the current strength changes in the conductor, the m.field changes, i.e. the magnetic flux created by this current changes. A change in the magnetic flux leads to the emergence of a vortex electric field and an induction EMF appears in the circuit. This phenomenon is called self-induction. Self-induction is the phenomenon of induction EMF in an electric circuit as a result of a change in current strength. The resulting emf is called the self-induction emf.

Manifestation of the phenomenon of self-induction

Closing the circuit When a circuit is closed, the current increases, which causes an increase in the magnetic flux in the coil, a vortex electric field arises, directed against the current, i.e. an EMF of self-induction occurs in the coil, which prevents the current from rising in the circuit (the vortex field slows down the electrons). As a result L1 lights up later, than L2.

Open circuit When the electric circuit is opened, the current decreases, there is a decrease in the m.flow in the coil, a vortex electric field appears, directed like a current (tending to maintain the same current strength), i.e. A self-inductive emf appears in the coil, which maintains the current in the circuit. As a result, L when turned off flashes brightly. Conclusion in electrical engineering, the phenomenon of self-induction manifests itself when the circuit is closed (the electric current increases gradually) and when the circuit is opened (the electric current does not disappear immediately).

INDUCTANCE

What does the EMF of self-induction depend on? Electric current creates its own magnetic field. The magnetic flux through the circuit is proportional to the magnetic field induction (Ф ~ B), the induction is proportional to the current strength in the conductor (B ~ I), therefore the magnetic flux is proportional to the current strength (Ф ~ I). The self-induction emf depends on the rate of change in the current strength in the electric circuit, on the properties of the conductor (size and shape) and on the relative magnetic permeability of the medium in which the conductor is located. A physical quantity showing the dependence of the self-induction EMF on the size and shape of the conductor and on the environment in which the conductor is located is called the self-induction coefficient or inductance. Inductance - physical. a value numerically equal to the EMF of self-induction that occurs in the circuit when the current strength changes by 1 ampere in 1 second. Also, the inductance can be calculated by the formula:

where F is the magnetic flux through the circuit, I is the current strength in the circuit.

SI units for inductance:

The inductance of the coil depends on: the number of turns, the size and shape of the coil, and the relative magnetic permeability of the medium (a core is possible).

SELF-INDUCTION EMF

EMF of self-induction prevents the increase in current strength when the circuit is turned on and the decrease in current strength when the circuit is opened.

To characterize the magnetization of a substance in a magnetic field, we use magnetic moment (P m ). It is numerically equal to the mechanical moment experienced by a substance in a magnetic field with an induction of 1 T.

The magnetic moment of a unit volume of a substance characterizes it magnetization - I , is determined by the formula:

I=R m /V , (2.4)

Where V is the volume of the substance.

Magnetization in the SI system is measured, like tension, in A/m, the quantity is vector.

The magnetic properties of substances are characterized bulk magnetic susceptibility - c O , the quantity is dimensionless.

If a body is placed in a magnetic field with induction IN 0 , then magnetization occurs. As a result, the body creates its own magnetic field with induction IN " , which interacts with the magnetizing field.

In this case, the induction vector in the environment (IN) will be composed of vectors:

B = B 0 + V " (vector sign omitted), (2.5)

Where IN " - induction of the own magnetic field of the magnetized substance.

The induction of its own field is determined by the magnetic properties of the substance, which are characterized by volumetric magnetic susceptibility - c O , the expression is true: IN " = c O IN 0 (2.6)

Divide by m 0 expression (2.6):

IN " /m O = c O IN 0 /m 0

We get: H " = c O H 0 , (2.7)

But H " determines the magnetization of a substance I , i.e. H " = I , then from (2.7):

I=c O H 0 . (2.8)

Thus, if the substance is in an external magnetic field with a strength H 0 , then inside it the induction is defined by the expression:

B=B 0 + V " = m 0 H 0 +m 0 H " = m 0 (H 0 +I)(2.9)

The last expression is strictly valid when the core (substance) is completely in an external uniform magnetic field (a closed torus, an infinitely long solenoid, etc.).

The flux of the magnetic induction vector B through any surface. The magnetic flux through a small area dS, within which the vector B is unchanged, is equal to dФ = ВndS, where Bn is the projection of the vector onto the normal to the area dS. Magnetic flux Ф through the final ... ... Big encyclopedic Dictionary

MAGNETIC FLUX- (flux of magnetic induction), flux Ф of the magnetic vector. induction B through c.l. surface. M. p. dФ through a small area dS, within which the vector B can be considered unchanged, is expressed by the product of the size of the area and the projection Bn of the vector onto ... ... Physical Encyclopedia

magnetic flux- A scalar value equal to the flux of magnetic induction. [GOST R 52002 2003] magnetic flux The flux of magnetic induction through a surface perpendicular to the magnetic field, defined as the product of magnetic induction at a given point and the area ... ... Technical Translator's Handbook

MAGNETIC FLUX- (symbol F), a measure of the strength and extent of the MAGNETIC FIELD. The flow through area A at right angles to the same magnetic field is Ф=mNA, where m is the magnetic PERMEABILITY of the medium, and H is the intensity of the magnetic field. The magnetic flux density is the flux ... ... Scientific and technical encyclopedic dictionary

MAGNETIC FLUX- flux Ф of the magnetic induction vector (see (5)) В through the surface S, normal to the vector В in a uniform magnetic field. The unit of magnetic flux in SI (see) ... Great Polytechnic Encyclopedia

MAGNETIC FLUX- a value characterizing the magnetic effect on a given surface. M. p. is measured by the number of magnetic lines of force passing through a given surface. Technical railway dictionary. M .: State transport ... ... Technical railway dictionary

magnetic flux- a scalar quantity equal to the flux of magnetic induction... Source: ELEKTROTEHNIKA. TERMS AND DEFINITIONS OF BASIC CONCEPTS. GOST R 52002 2003 (approved by the Decree of the State Standard of the Russian Federation of 01/09/2003 N 3 st) ... Official terminology

magnetic flux- the flux of the magnetic induction vector B through any surface. The magnetic flux through a small area dS, within which the vector B is unchanged, is equal to dФ = BndS, where Bn is the projection of the vector onto the normal to the area dS. Magnetic flux Ф through the final ... ... encyclopedic Dictionary

magnetic flux- , flux of magnetic induction flux of the vector of magnetic induction through any surface. For a closed surface, the total magnetic flux is zero, which reflects the solenoid nature of the magnetic field, i.e., the absence in nature of ... Encyclopedic Dictionary of Metallurgy

magnetic flux- 12. Magnetic flux Flux of magnetic induction Source: GOST 19880 74: Electrical engineering. Basic concepts. Terms and definitions original document 12 magnetic on ... Dictionary-reference book of terms of normative and technical documentation

Books

• , Mitkevich V. F. This book contains a lot that is not always paid due attention when it comes to magnetic flux, and that has not yet been sufficiently clearly expressed or has not been ... Buy for 2252 UAH (only Ukraine)
• Magnetic flux and its transformation, VF Mitkevich. This book will be produced in accordance with your order using Print-on-Demand technology. There is much in this book that is not always given due attention when it comes to…